ELECTROMAGNETIC ELECTRON-ELECTRON FORCE
By Prof. L. Kaliambos (Natural Philosopher in New Energy) February 27, 2015 Despite the enormous success of the Bohr model (1913) and the Schrodinger equation (1926) based on the well-established electromagnetic laws in explaining the principal features of the spectrum of one-electron atomic systems, neither was able to provide a satisfactory explanation of the chemical properties of atoms for forming molecules and atoms with many electrons, because the discovery of the electron spin gives a peripheral velocity greater than the speed of light, which was believed to be incorrect under the influence of Einstein’s special relativity. (Faster than light). Therefore physicists developed theories of the so-called qualitative symmetric properties including not the well-established laws of real magnetic attractions between the two electrons of opposite spin but wrong forces like those of Heisenberg’s theory of Exchange Interaction. It is indeed unfortunate that today many physicists under the influence of the invalid relativity continue to believe in the fallacious Exchange Interaction.Under this physics crisis I published my paper "Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures" (2008) in which I showed that two electrons of opposite spin at very short interelectron separation exert stronger magnetic attraction than the electric repulsion For example in the simplest Helium atom the two electrons of oposite spin behave like one particle of charge (-2e). In fact, after the discovery of the electron spin by Uhlenbeck and Goudsmit (1925), which gives velocities greater than the speed of light (u>>c), I applied the well-established laws of electric and magnetic interactions and I found that this situation is responsible for magnetic attractions of short range between two electrons, which overcome the electric repulsions of long range at short inter-electron separations. According to the well-established laws of Coulomb (1785) and the Ampere (1820) and also the experiments of the Quantum Entanglement (1935) such electromagnetic forces act at a distance. However today many physicists under the influence of wrong theories of Maxwell and Einstein believe in the FALSE FEYNMAN DIAGRAMS of the wrong theory of force carriers. For example in the “Force carrier-WIKIPEDIA” one reads: “In particle physics, force carriers are particles that give rise to forces between other particles. These particles are bundles of energy (quanta) of a particular kind of field. There is one kind of field for every species of elementary particle. For instance, there is an electron field whose quanta are electrons, and an electromagnetic field whose quanta are photons. The force carrier particles that mediate the electromagnetic, weak, and strong interactions are called gauge bosons.” It is well-known that in 1925 Goudsmit and Uhlenbeck discovered the electron spin S = s(s+1)0.5 (h/2π) where s = ½ This fact which gives a peripheral velocity u greater than the speed of light (u >> c ) invalidates Einstein’s relativity. Note that the velocity u of the electron spin cannot be related to the velocity v of the kinetic energy of the electron when it absorbs the energy hν of photons. For example in the Correct Explanation of Photoelectric Effect though photons of mass m = hν/c2 move at the speed of light c, the electrons of mass M cannot move at the speed of light because in the experiments of Kauffmann (1901) after the absorption of the energy hν one observes the following expression M/Mo = c/ (c2- v2)0.5 It means that an electron with a variable mass M cannot move as fast as the speed of light c, because the electron of a constant inertial mass Mo (before the absorption) absorbs the mass m = hν/c2 of photons and becomes an electron with a variable mass M. So under the important condition of the intrinsic electron spin which differs fundamentally from the Correct Explanation of Photoelectric Effect in my paper “Spin- spin Interactions ofelectrons and also of nucleons create atomic molecular and nuclear structures” ( Ind. J. Th. Phys. 2008) , I discovered that the velocity (u >>c ) of spinning electrons gives stronger magnetic attraction than the electric repulsion at an inter-electron separation r < 578.8/1015 m. For two interacting electrons with charge (-e) at a distance r taking into account the successful application of the basic Coulomb law in the Schrodinger equation I applied the fundamental laws of Coulomb and Biot-Savart on the charges of spinning electrons. Note that the magnetic interactions give S = 0. Because of the antiparallel spin along the radial direction the interaction of the electron charges of (-e) gives a repulsive electric force Fe = Ke2/r2 of the Coulomb law. Moreover in my research of my published paper "Nuclear structure is governed by the fundamental laws of electromagnetism"( 2003) the integration for calculating the attractive magnetic force Fm led to the following expression: Fm = (Ke2/r4)(9h2/16π2M2c2) Where K is the constant of the Coulomb law because the constant k of the magnetic force is given by k = K/c2 . Then h is the Planck constant, M is the mass of the electron, and c is the velocity of light. Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force Fem = Fe - Fm . Therefore in my research the integration for calculating the mutual electromagnetic force led to the following relation: Fem = Fe – Fm = Ke2/r2 - (Ke2/r4)(9h2/16π2 M 2c2) Of course for Fe = Fm one gets the equilibrium separation ro = 3h/4πMc = 578.8/1015 m. That is, for r < 578.8/1015 m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive Fm is stronger than the repulsive Fe . Here Fm is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron in nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S = 0) but parallel ( S = 1). According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin ( S = 1) with electric and magnetic repulsions given by Fem = Fe + Fm So according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/1015 m a motional EMF produces vibrations of paired electrons. Unfortunately today in the absence of a detailed knowledge physicists believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper of 2008 I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as Ev = 16.95Z - 4.1 Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as E = -27.2 Z2. So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by E = - 27.2 Z2 +16.95 Z - 4.1 For example the laboratory measurement of the ionization energy of H- yields an energy of the ground state E = - 14.35 eV . In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV. So in the absence of such a detailed knowledge, great theoretical physicists, under the strong influence of the invalid relativity, abandoned the natural laws of electromagnetism and developed theories with qualitative approaches. Following the work, of Pauli (1925) who suggested the qualitative exclusion principle for two electrons of opposite spin, chemists studied the chemical properties of numerous compounds. Though their efforts shed much light on the subject, the fundamental nature of the forces that hold atoms together to form the simplest hydrogen molecule remained mysterious. For example about 1927 great scientists like Heitler, London, Born, Oppenheimer, and later, Pauling, and others, under the abandonment of natural laws of electromagnetism applied without success the new techniques of the quantum mechanics to the problem. Under such a crisis a new Molecular Orbital Theory was developed in the years after the qualitative valence bond (1927) primarily through the efforts of Hund and Muliken. In the Molecular Orbital Theory, atoms form bonds by sharing electrons. That is, in the absence of a real attractive force based on natural laws, atomic orbitals combine theoretically to form molecular orbitals. Similar to atomic orbitals, molecular orbitals were assumed to be wave functions giving the probability of finding an electron in certain regions of a molecule. Each molecular orbital can only have 2 electrons, each with an opposite spin. The hydrogen molecule for example was assumed to have two molecular orbitals, an antibonding orbital and a bonding orbital. However the theory cannot explain how the atomic orbitals overlap, to give an increase in electron density and therefore an increase in the intensity of the negative charge. In fact, an attractive magnetic force contributes to the increase in negative charge which causes the nuclei to be drawn closer together. Due to the lower potential energy in molecular bonds than in separate atomic orbitals, it is more energy efficient for the electrons to stay in a molecular bond rather than be pushed back into the 1s orbitals of separate atoms. This is what keeps bonds from breaking apart. However in the absence of such a detailed knowledge today the Molecular Orbital Theory is applied in a manner using sum empirically derived parameters. DISCOVERY OF THE BINDING ENERGY OF THE SIMPLE HYDROGEN MOLECULE BASED ON THE ELECTROMAGNETIC ELECTRON-ELECTRON FORCE In the correct hydrogen molecule the two electrons of opposite spin (S = 0) behave like one particle circulating about the two separated nuclei with opposite spin under the rules of quantum mechanics. In this bonding state we neglect the very small magnetic attraction between the two spinning protons of opposite spin. If the protons are well separated the system of two electrons with S =0 will be bound to one or the other. The ground state energy in eV in each proton is then given by E = -27.2 Z2 + 16.95 Z - 4.1 eV. Since Z = 1 one gets E = -14.35 eV As the proton-proton separation is reduced, the wave function is altered since the system of two electrons of opposite spin feels the electrostatic potential of both protons. For example in the case of the Helium atom we apply the above equation for Z = 2 and get E = - 79 eV However in the case of the hydrogen molecule the detailed experiments showed that the separation of the two protons is ro = 0.74/1010 m which yield a positive potential E(pp) in eV given by E(pp) = Ke/ro = 14.4/0.74 = 19.46 eV In this case the system of two electrons of opposite spin feels not the electrostatic potential of the charge Ze = 2e but the potential of the effective charge ζe where 1 < ζ < 2. Thus we write E = -27.2 ζ2 +16.95 ζ - 4.1 + 19.46 eV Since the detailed calculations of the experiments yield E = -31.68 eV we may write 27.2 ζ2 -16.95ζ - 47.04 = 0. Then solving for ζ one gets ζ = 1.663. CONCLUSIONS The successful discovery of the electron spin which gives a peripheral velocity u greater than the speed of light (u>>c) under the influence of the invalid relativity led to the abandonment of the well-established laws of electromagnetism. Note that the well-established laws of Coulomb and Newton were applied for the enormous success of the Bohr model and the Schrodinger equation. (See my BOHR AND SCHRODINGER REJECT EINSTEIN and NEWTON INVALIDATES EINSTEIN ). In fact. the peripheral velocity (u >> c) of spinning electrons gives a magnetic attraction of short range between the two electrons of opposite, spin which overcomes the electric repulsion of long range at a short inter-electron separation. Category:Fundamental physics concepts